<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC
 "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN"
 "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<title>pi-qmc: Introduction</title>
<meta charset="UTF-8" />
<link rel="stylesheet" href="pi.css" type="text/css"/>
<script type="text/javascript" src="pagecontents.js"></script>
</head>

<body>
<div class="nav">
<a href="index.xhtml" class="up">Contents</a>
<a href="Overview.xhtml" class="next">Overview</a>
</div>
<h1>Introduction</h1>
<p>
This is a quantum simulation program from the Shumway Research Group, 
which focuses on applications to nanoscience and technology. 
Path integral Monte Carlo (PIMC) simulates particles (often electrons 
and ions) by directly sampling the canonical partition function. 
In the path integral formulation of quantum statistical mechanics 
developed by Richard Feynman, particles get represented by closed 
imaginary-time trajectories of length ℏ/kT. PIMC simulations are 
able to compute total energies, correlation functions, charge 
distribution, and linear response functions for thermal equilibrium. 
As in many quantum Monte Carlo methods, PIMC has efficient scaling 
with system size, often order N<sup>2</sup> or N<sup>3</sup>.</p>

<p>Our application, <span class="pi">pi</span> 
is well suited for modeling conduction electrons and holes 
in quantum dots, quantum wires, and quantum wells. 
For quantum dots and wires, we often generate realistic confining 
potentials using 
<a href="http://code.google.com/p/qdot-tools">qdot-tools</a>.
We are also testing and developing 
<span class="pi">pi</span> for ab initio calculations, but at this point only 
hydrogen and helium systems work well.</p>

</body>
</html>

